Question

Suppose that you flip 4 coins. How many items are in the sample space? 16 What is the probability that all four coins come up heads? (Write your answer numerator/denominator) 4/16 What is the probability that you get exactly 2 heads? 2/16

Answer 1

Suppose that you flip 4 coins. The sample space consists of 16 different Sequences and all are equally likely with a probability = 76 - - Sample space is -S= HHHH), CHHHT),(HHIH) CHHILL, (HTHH), (H THT), (HTT 1), (HTTI), (THHH), THTH), LJ HHT), UHTI), (THH), TT HT), (TITH), (TTI) } Number of elements in s n(s)=16__ is 16 of items in the sample Therefore the number space is 16_ " What is the probability that all four coins - come up_heads. Let event A : 011 fower coios come up beads A CHHHH) } pucaber of elements in DBL nCAEL A PCA)= number of elements in number of elements in s PCA SI - OCA) n ls)

4 four coins Therefore probability that all come up beads is_TG 1) What is the probability that you get - exactly 2 heads _Let event B.:_Exactly 2 beses to flip of 4 Cols- B= {(HHTI), (HIHI), CHITH), QHTH), GHHIL, QIHH)} number of elements in B = 6 . n(B) = 6 .PCB) = number of elements in B number of elements_jos_ = n(B) (s) 63 16 P(B) = 3 Therefore, Probability that you get exactly -_2 beads is a