"And and Or" probability questions. the table shows the probability of rain of the next three days:
Friday 90%
Saturday 90%
Sunday 90%
work out the probability that it will rain on exactly two consecutive days

Probability that it will rain on two consecutive days = 0.162

Explanation:

Assuming that the events are independent events.

The probability that it will rain on exactly two consecutive days between Friday and Sunday involves two outcomes:

1) either it does not rain on Sunday, but it rains on Friday and Saturday, or

2) it does not rain on Friday, and then it rains on Saturday and Sunday

The probability that it will rain on Friday and Saturday, but not on Sunday is

P(Fri)*P(Sat)*P(not Sun)

P(Fri) = 0.9, P(Sat) = 0.9; P(not Sun) = 1 - 0.9 = 0.1

Therefore, the probability = 0.9 * 0.9 * 0.1 = 0.081

Also, the probability that it will rain on Saturday and Sunday, but not on Friday is;

P(Sat)*P(Sun)*P(not Fri)

P(Sat) = 0.9; P(Sun) = 0.9; P(not Fri) = 1 - 0.9 = 0.1

Therefore, the probability = 0.9*0.9*0.1 = 0.081

Therfore, the probability that it will rain on exactly two consecutive days between Friday and Sunday = 0.081 + 0.081 = 0.162