M230 Test II Fall 1998Solutions

1.

(a)

(b) T = the event the # of heads obtained was 2
F = event the first toss was a head

2.
red ball drawn on the ith draw
green ball drawn on the ith draw

(a)

(b)

(c)
so

3. Using Bernoulli trials with n = 3

(a)

(b)

(c)

(d) E(4X + 5) = E(4x) + E(5) = 4 E(X) + 5 = 9 + 5 = 14

4. Let Bill's rate in mph
Mike's rate in mph
Since Bill travels 6 mph faster than Mike,

If Bill travels for 5 hours and Mike travels 2 hours longer, then Mike travels for 7 hours.
Since distance = rate time :

AND
substituting for in the first equation :


And now substituting back into the second equation we get

So Mike is traveling at 15 mph and Bill is traveling at 21 mph. This is unreasonably fast for bicycling for 5 and 7 hours.

5.let X = # of successes of 5 rolls
W = X - 1

so

You are expected to lose in the long run. You should not play the game.