Question

Determine whether the events described in each exercise are independent or dependent. Then find the and probability of the events.

1.) Tossing a coin four times in a row and getting HTHT, in that order?

2.) The next five births at a hospital all being boys?

Determine whether the events described in each exercise are overlapping or non-overlapping. Then find the either/or probability of the events.

1.) Getting a sum of either 5 or 9 on a roll of two dice?

2.) Drawing either a 10 or a heart from a regular deck of cards?

Answer 1

1)

a)

Tossing a coin is independent of before toss

Sample space contains 16 possibilites as we are tossing the for 4times

We want probability of HTHT =1/16

b)

Giving birth to boy child is independent of before birth

Probability of giving birth to boy child =1/2

Probability of giving birth to 5 boys consecutively will be (1/2)^5=1/32

2)

let PCA) is probability of event a P(B) is probability of events for Non ovel lapping = PAI+P(B) P(AUB) lapping for over PCA) +PCB) -P(ANB) PCAUB) @ Getting sum eithel sora on two dice. det. A be event getting sums Total no. of possible cases for 5 = (1/4)(4,4) (2,3) (3,2) 4 36 is total sampled space space) for twodice roll Let B be event gettin Sum q. =) P(A) { 36 36. Possible. Coses < 4,516,0) 6,3) 63,0 =) P(B) 36. These events all non-overlapping =) P(AUB) = 4 + 4 36 36 = 2 allo

PCA) be dlaw "10" from deck of calds. ale ہا (there 4 10 calds) =) P(A) 52 =) P(B) be probabilit to draw Heald -) P(B) = 13 (thele ale 13" Healts") 52 one to cald in - (there will P(ANB) - healt) 052 P(A) + PCB) - P(ANB) P(AUB) 4 + 13-) 52 52 52 16 32 These two all overlapping events