1.袋中有5个红球和5个绿球,现掷一枚均匀骰子,掷出几点就从中随机取几个球.若任意投掷一个骰子袋中有5个红球和5个绿球,现掷一枚均匀骰子,掷出几点就从中随机取几个球.若任意投掷一个骰

Question

1.袋中有5个红球和5个绿球,现掷一枚均匀骰子,掷出几点就从中随机取几个球.若任意投掷一个骰子
袋中有5个红球和5个绿球,现掷一枚均匀骰子,掷出几点就从中随机取几个球.若任意投掷一个骰子.求（1）取出全是红球概率（2）若已知取出全红球,求掷出3点概率

Answer 1

5R, 5G
(1)
P(all red)
=P(toss 1 and 1R )+ P(toss 2 and 2R)+ P(toss 3 and 3R) +P(toss 4 and 4R)+P(toss 5 and 5R)
=(1/6) [ 5/10 + (5/10)(4/9) +(5/10)(4/9)(3/8) +(5/10)(4/9)(3/8)(2/7) +(5/10)(4/9)(3/8)(2/7)(1/6) ]
=(1/12)[ 1+4/9 +(4/9)(3/8) +(4/9)(3/8)(2/7) +(4/9)(3/8)(2/7)(1/6) ]
=(1/12)[ 1+ (1344+504+144+24)/3024 ]
=5/72
P(all red| toss 3)
=P(3R)/P(toss 3)
= (5/10)(4/9)(3/8)
=1/12