I have three questions about counting.

About # 3, I am not confident in my answer. Could you check if it is correct?

About # 7, I am not sure I could solve the "given that" question. Could you check my answer?

About #9, I could get the answer for exactly 50 heads, but I could not get less than 50 heads. Could you give me some advice to solve the problem?

Thanks,

7. (10pts) You are dealt two cards face down from a well-shuffled 52-card deck. The deck contains exactly four aces. (a) (5pts) You reveal the two cards at the same time. What is the probability that both of your cards are aces?7. (a). 4 C2/ (52 C 2) = 1/ 221 A. 1/221 (b). E is the event that the first card is an ace. F is the event that the second card is an ace. P (E) = 4/52 P (F) = 3/51 P(EnF) = P(E) *P (F) Therefore, P(EnF) / P(E) =P (E) * P (F) /P (E) = P (E) = 4/ 52 = 1/ 139. (10pts) You are given a biased coin which comes up heads with probability 0.7. You toss the biased coin 100 times. What is the probability that you get less than or equal to 50 heads?(b) (5pts) You reveal one card first, and the card is an ace. Given that, what is the probability that the second card is also an ace?9. P (H) = 0.7 P (T) = 0.3 The probability of getting exactly 50 heads. C(50, 100) * (0.7)^ 50 * (0.3)~ 50 10. In the experiment, the possible ways are ( T HH HH ), (HT HH HH), ( H HT HH HH), (H HH T HHHH). Since it is a fair coin, P (H) and P (T) are 1/2. B Therefore, 1 226 A. 1 2263. (10pt5) Haw many ways are there to tall 3 fair Eided dice 6 times and obtain an outcome with one 11, three 55, and twn 155? \f