Sajjad1994 wrote:
At an end-of-year party for the employees of a certain company, Martha has been given an opportunity to win as many as two prizes. She must draw, at random, exactly one numbered card from each of two boxes—each of which, in turn, contains exactly six cards, numbered from 1 to 6. If the sum of the two numbers is equal to 8, then Martha will win a tablet computer. And, if at least one of the two numbers is a 2, then Martha will win a smartphone.
Select the probability that Martha will win a Tablet computer, and select the probability that Martha will win Both prizes. Make only two selections, one in each column.
To calculate the probability of winning a tablet computer, we need to find the number of ways of getting a sum of 8.
8 = 2+6 = 3+5 = 4+4
P(2+6) = 1/6 * 1/6 * 2 = 2/36 (we multiply by 2 because she could draw the card 2 from either box and the 6 from the other)
Same will be the probability of obtaining 3+5 but for 4+4 we will not multiply by 2 (because the numbers are same, 4 each)
Hence Total Probability = 2/36 + 2/36 + 1/36 = 5/36
Now probability of winning both will be less than 5/36 (the probability of winning just the tablet).
The only value less than 5/36 is 1/18.
ANSWER: 5/36, 1/18If you need to calculate the probability of both, notice that she needs (2+6) or (3+5) or (4+4) to get a tablet and she will also win the phone only if she gets (2+6). Hence the probability of winning both is simply the probbaility of getting (2+6) which is 2/36.
Check the discussion on Probability here:
https://youtu.be/0BCqnD2r-kY