Question

The turnout of spectators at the world cup cricket match is dependent upon the

weather. On a rainy day the probability of a big turnout is 0.3. If it doesn’t rain,

then the probability of big turnout increases by 0.6. The weather forecast gives a

probability of 0.75 that it will rain on the day of the match.

Find the probability that (i) there is a big turn out and it rains (ii) there is a big turn

out.​

Answer 1

The probability that there is a big turn out and it rains is 0.225 and the probability of a big turn out in general is 0.9

Step-by-step explanation:

• In this case,the probability of big turn out or P(B) is dependent on probability of a rainy day or P(R).
• The probability of a big turn out on a rainy day is 0.3 and the probability of big turn out if it doesn't rain is 0.6.Therefore, the probability of a big turn out or P(B)=$0.3+0.6=0.9$.
• Now,the probability of rain or P(R) according to the weather forecast is 0.75.
• Hence,the joint probability or big turn out and rain or P(B and R)=$0.75\times 0.3$=0.225.