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One letter is selected at random from the 5 letters V, W, X, Y, and Z,
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24 May 2020, 07:28
Question Stats:
49% (02:25) correct 51% (02:21) wrong based on 57 sessions
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One letter is selected at random from the 5 letters V, W, X, Y, and Z, and event A is the event that the letter V is selected. A fair sixsided die with sides numbered 1, 2, 3, 4, 5 and 6 is to be rolled, and event B is the event that a 5 or a 6 shows. A fair coin is to be tossed, and event C is the event that a head shows. What is the probability that event A occurs and at least one of the events b and c occurs A. 1/30 B. 1/15 C. 1/10 D. 2/15 E. 1/5
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One letter is selected at random from the 5 letters V, W, X, Y, and Z,
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24 May 2020, 07:35
rakshitsood21 wrote: One letter is selected at random from the 5 letters V, W, X, Y, and Z, and event A is the event that the letter V is selected. A fair sixsided die with sides numbered 1, 2, 3, 4, 5 and 6 is to be rolled, and event B is the event that a 5 or a 6 shows. A fair coin is to be tossed, and event C is the event that a head shows.
What is the probability that event A occurs and at least one of the events b and c occurs
A. 1/30 B. 1/15 C. 1/10 D. 2/15 E. 1/5 One letter is selected at random from the 5 letters V, W, X, Y, and Z, and event A is the event that the letter V is selected.  \(\frac{1}{5}\) A fair sixsided die with sides numbered 1, 2, 3, 4, 5 and 6 is to be rolled, and event B is the event that a 5 or a 6 shows. \(\frac{2}{6}=\frac{1}{3}\) A fair coin is to be tossed, and event C is the event that a head shows.\(\frac{1}{2}\) Now we are looking for 'the probability that event A occurs and at least one of the events b and c occurs' Probability that both A and B occur  \(\frac{1}{5}*\frac{1}{3}\) Probability that both A and B occur  \(\frac{1}{5}*\frac{1}{2}\) Probability that all three A, B and C occur  \(\frac{1}{5}*\frac{1}{2}*\frac{1}{3}\)... Now this is part of both the above probabilities.Answer = \(\frac{1}{5}(\frac{1}{2}+\frac{1}{3}\frac{1}{2}*\frac{1}{3})=\frac{1}{5}*\frac{2}{3}=\frac{2}{15}\) D
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Re: One letter is selected at random from the 5 letters V, W, X, Y, and Z,
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24 May 2020, 14:21
chetan2u wrote: rakshitsood21 wrote: One letter is selected at random from the 5 letters V, W, X, Y, and Z, and event A is the event that the letter V is selected. A fair sixsided die with sides numbered 1, 2, 3, 4, 5 and 6 is to be rolled, and event B is the event that a 5 or a 6 shows. A fair coin is to be tossed, and event C is the event that a head shows.
What is the probability that event A occurs and at least one of the events b and c occurs
A. 1/30 B. 1/15 C. 1/10 D. 2/15 E. 1/5 One letter is selected at random from the 5 letters V, W, X, Y, and Z, and event A is the event that the letter V is selected.  \(\frac{1}{5}\) A fair sixsided die with sides numbered 1, 2, 3, 4, 5 and 6 is to be rolled, and event B is the event that a 5 or a 6 shows. \(\frac{2}{6}=\frac{1}{3}\) A fair coin is to be tossed, and event C is the event that a head shows.\(\frac{1}{2}\) Now we are looking for 'the probability that event A occurs and at least one of the events b and c occurs' Probability that both A and B occur  \(\frac{1}{5}*\frac{1}{3}\) Probability that both A and B occur  \(\frac{1}{5}*\frac{1}{2}\) Probability that all three A, B and C occur  \(\frac{1}{5}*\frac{1}{2}*\frac{1}{3}\)... Now this is part of both the above probabilities.Answer = \(\frac{1}{5}(\frac{1}{2}+\frac{1}{3}\frac{1}{2}*\frac{1}{3})=\frac{1}{5}*\frac{2}{3}=\frac{2}{15}\) D Hi chetan2uWhy did you subtract all three events together?



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Re: One letter is selected at random from the 5 letters V, W, X, Y, and Z,
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24 May 2020, 18:36
Hi chetan2u , did not understand the substraction part. Kindly help



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Re: One letter is selected at random from the 5 letters V, W, X, Y, and Z,
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24 May 2020, 18:53
Aman1204 and KunniWhen we are looking at A and B happening together, it includes when C happens with them. Similarly when we are looking at A and C happening together, it includes When B happens with them. So when you add both the above cases, all three happening together is added two times, so we have to subtract it once from the total.
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Re: One letter is selected at random from the 5 letters V, W, X, Y, and Z,
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24 May 2020, 21:09
we have to find the probability of A and (B or C).
Now B or C means 1  (!B and !C) = 1  [(2/3)*(1/2)] = 2/3.
multiplying by probability of A we get 2/15.



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Re: One letter is selected at random from the 5 letters V, W, X, Y, and Z,
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25 May 2020, 23:11
Hi chetan2u, There is a typo: Probability that both A and B occur  1/5∗1/2 Probability that both A and C occur  1/5∗1/2



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Re: One letter is selected at random from the 5 letters V, W, X, Y, and Z,
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26 May 2020, 07:02
P(required) = P(A)*(1 P(not B)*P(not C)) = 1/5 * (1  [4/6 * 1/2]) = 2/15 > D




Re: One letter is selected at random from the 5 letters V, W, X, Y, and Z,
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26 May 2020, 07:02




