Answer:
A.) 0.7647 b.) 13/ 16 C.) 0.9412 D.) 8.743 * 10^-10
Step-by-step explanation:
A)
Number of cards per suit = 13
Nunber of suits = 4
Probability = required outcome / Total possible outcomes
P(1) = probability of picking a card from a certain suit
P(1) = 13 / 52
Hence, probability that 2nd card will be from a suit different from the first :
Total possible outcomes = (52 - 1) = 51
Required outcomes = (13 * 3) = 39
= 39 / 51
= 0.7647
B.)
First toss being head :
Required outcome = H = 1
Total possible outcomes = T or H = 2
P(H) = 1/ 2
For 5 tosses
Total possible outcomes = 2^n = 2^5 = 32
Exactly 2 heads = 10
P(exactly 2 heads) = 10/32 = 5/16
1/2 + 5/16 = (8 + 5) / 16 = 13/16
c)
1 - P(both top and bottom are hearts)
Number of hearts = 13 ; number of cards = 52
P(both are hearts) = 13/52 * 12/51 = 0.05882
1 - 0.05882
= 0.94117
= 0.9412
d)
Either all marbles are red OR all marbles are green OR all marbles are blue
Total number of marbles = (20 + 20 + 20) = 60
Probability that all 15 marbles are of a certain color :
(20/60 * 19/59 * 18/58 * 17/57 * 16/56 * 15/55 * 14/54 * 13/53 * 12/52 * 11/51 * 10/50 * 9/49 * 8/48 * 7/47 * 6/46)
(2.9146E−10) + (2.9146E−10) + (2.9146E−10)
= 8.7438E−10
= 8.743 * 10^-10
