ill give 1500 points if you answer 31Solutiona Yes the even

ill give 1500 points if you answer

# 31

Solution

a) Yes, the events \"diameter is between 4 and 6\" and \"diameter is between 8 and 12\" are mutually exclusive events.

Mutually Exlcusive Events: Two events are mutually exclusive if they cannot occur at the same time.

Here, the diameter can\'t falls in both the regions (4 and 6) and (8 and 12). Only one of the event is possible at a time. Hence, both the events are mutually exclusive.

b) Let X be the diameter.

From the figure 1 : P(4 < X < 6) = 0.14

From the figure 2 : P(10 < X < 12) = 0.14

From the figure 3 : P(8 < X < 12) = 0.48

From the figure 4 : P(12 < X < 14) = 0.02

Now, P( X lies in (4 - 6) or X lies in (8 - 12) )

= P(4 < X < 6) + P(8 < X < 12)

= 0.14 + 0.48

= 0.62