Please solve asap possible.I would really appreciate your help . Thanks Three (6
ID: 3270943 • Letter: P
Question
Please solve asap possible.I would really appreciate your help .
Thanks
Three (6-sided) dice are thrown. a) What is the probability that the same number appears on all three dice? b) On exactly two of the dice? A family has two children. Any child is equally likely to be a boy or a girl. a. What is the probability of 2 boys, 2 girls, and 1 boy and 1 girl (in either order)? b. What is the probability that both are girls given that the eldest is a girl? c. What is the probability that both are girls given that at least one is a girl? A deck of 52 playing cards is randomly shuffled and divided into 4 piles of 13 cards each. Define E_i as the event that pile i contains exactly one ace. d. What is P(E_1)? e. What is the probability that each pile has exactly one ace?Explanation / Answer
According to Chegg policy only four subquestions will be solved. Please post the remaining in another question)
4. a) Each die can have 6 values. Therefore, the total number of possibilities = 6*6*6 = 216
There are 6 ways in which the same number appears on top of the three dice and they are (1,1,1),(2,2,2),(3,3,3),(4,4,4),(5,5,5),(6,6,6).
Thus the probability is 6/216 = 1/36 = 0.028.
b) There are 6 ways in which two dice can have the same number. Further the two dice which show the same number can come in 3C2 ways. And foe each of the combinations, the value on the third dice should be different i.e there are 5 combinations.
Thus the total number of combinations = 6 * 3C2 * 5 = 6 * 3 * 5 = 90
Probability = 90/216 = 0.42
5. a) The probability that the first child is a boy = 1/2
The probability that the second child is also a boy = 1/2
Therefore, the probability that both children are boys = 1/2 * 1/2 = 1/4.
The probability that the first child is a girl = 1/2
The probability that the second child is also a girl = 1/2
Therefore, the probability that both children are girls = 1/2 * 1/2 = 1/4.
The probability that one child is a boy and the other is a girl = 1 - 1/4 - 1/4 = 1/2.