Determine the probability he will buy an ice cream on Wednesday.

Question

When walking home from school during the summer months, Harold buys either an ice-cream or a drink from the corner shop. If Harold bought an ice-cream the previous day, there is a 30% chance that he will buy a drink the next day. If he bought a drink the previous day, there is a 40% chance that he will buy an ice-cream the next day. On Monday, Harold bought an ice-cream. Determine the probability that he buys an ice-cream on Wednesday.

Answer 1

We know he bought an ice cream on Monday

So the possibilities are

Tuesday Wednesday Tues prob Wed prob Prob of both

Ice Drink 0.70 0.30 0.7 x 0.3 = 0.21

Ice Ice 0.70 0.70 0.49

Drink Ice 0.30 0.40 0.12

Drink Drink 0.30 0.60 0.18

So probability (ice on Wed) = 0.49 + 0.12 = 0.61

Can also use a probability tree diagram here