Leo toses 3 coins once in a certain game. Suppose tossing the coins to obtain 3 heads gets an award of 50 coupons, 2 heads gets 10 coupons, 1 head gets 5 coupons but no head will lose 100 coupons.
a) Find the probabilities that Leo gets 3 heads, 2heads and 1 head.
b) Find the expected value of award he can get in one game.
Probability
2006-11-19 4:33 pm
回答 (2)
2006-11-19 4:51 pm
✔ 最佳答案
a) 3 heads = 1/2 x 1/2 x 1/2 = 1/82 heads = 1/2 x 1/2 x 1/2 x 3 = 3/8
1 heads = 1/2 x 1/2 x 1/2 x 3 = 3/8
b) expected value of get award in one game = 3 heads + 2 heads + 1 heads
= 1/8 + 3/8 +3/8 = 7/8
2006-11-19 5:20 pm
(a)
the probabilities that Leo gets 3 heads
=P(head,head,head)
=1/2*1/2*1/2
=1/8
the probabilities that Leo gets 2heads
= P(head, head,tail)+P(head,head,tail)+P(head,tail,head)
=(1/2*1/2*1/2)*3
=3/8
the probabilities that Leo gets 1heads
=P(head, tail,tail)+P(tail,head,tail)+P(tail,tail,head)
=(1/2*1/2*1/2)*3
=3/8
(b)
the probabilities that Leo gets 0 heads
=P(tail,tail,tail)
=1/2*1/2*1/2
=1/8
the expected value of award he can get in one game
=50*P(gets 3 heads)+10*P(gets 2 heads)+5*P(gets 1 head)-100*P(gets 0 head)
=50*1/8+10*3/8+5*3/8-100*1/8
=(50+30+15-100)/8
=-5/8
For average, in one game, he will lose 5/8 coupons
the probabilities that Leo gets 3 heads
=P(head,head,head)
=1/2*1/2*1/2
=1/8
the probabilities that Leo gets 2heads
= P(head, head,tail)+P(head,head,tail)+P(head,tail,head)
=(1/2*1/2*1/2)*3
=3/8
the probabilities that Leo gets 1heads
=P(head, tail,tail)+P(tail,head,tail)+P(tail,tail,head)
=(1/2*1/2*1/2)*3
=3/8
(b)
the probabilities that Leo gets 0 heads
=P(tail,tail,tail)
=1/2*1/2*1/2
=1/8
the expected value of award he can get in one game
=50*P(gets 3 heads)+10*P(gets 2 heads)+5*P(gets 1 head)-100*P(gets 0 head)
=50*1/8+10*3/8+5*3/8-100*1/8
=(50+30+15-100)/8
=-5/8
For average, in one game, he will lose 5/8 coupons
收錄日期: 2021-04-25 16:50:29
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