Tanisha2819 wrote:
CareerGeek wrote:
Formula: Probability of getting r heads when coin is tossed n times = nCr*\(p^r*q^{n-r}\)
Where p = probability of getting heads
& q = probability of getting tails
Probability(at least 2 heads) = 1 - Probability(0 heads or 1 head)
Probability (0 heads) = \(5C_0*(1/2)^5 = 1/32\)
Probability (1 head) = \(5C_1*(1/2)^5 = 5/32\)
Probability(0 heads or 1 head) = \(1/32 + 5/32 = 6/32 = 3/16\)
—> Required Probability = \(1 - 3/16 = 13/16\)
IMO Option D
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Hello!! Could an expert please explain here that why are we multiplying both the cases by 5c0 & 5c1 in the case of 0 heads and 1 head respectively.
Would really appreciate any help here.
Thank you
Bunuel @
e-gmat KarishmaB @chetan4u
Bunuel@
e-gmatKarishmaB@chetan4u
I remember studying various such formulae in my 12th grade but I have never needed any of them for a GMAT question.
When you toss a coin 5 times, you can get 2^5 = 32 different outcomes. such as HHTHH, TTHHH, THTHH etc.
Now you need those in which you have at least 2 Heads. It is easier to find the probability of getting 0 Hs or 1 H.
In how many ways do you get 0 Hs? In 1 way TTTTT
In how many ways do you get 1 H? In 5 ways because TTTTH can be arranged in 5 ways (H can take any one of the 5 spots). TTTTH or TTTHT or TTHTT or THTTT or HTTTT
(This is also the reason why we multiply by 5C1 in the formula)
Hence 6 of the 32 cases are not acceptable so 26 cases are.
Required Probability = 26/32 = 13/16
Answer (D)
Also check these:
Video on Permutations:
https://youtu.be/LFnLKx06EMUVideo on Combinations:
https://youtu.be/tUPJhcUxllQVideo on Probability:
https://youtu.be/0BCqnD2r-kY