There are 8 jelly beans in a bag. the probability of randomly picking two orange jellybeans without replacement is 3/14. how many orange jellybeans are in the bag?

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Answer 1 · 2018-05-21T07:06:58

# 4#.

Suppose that, there are #n# orange jellybeans in the bag.

Out of these, #2# orange jellybeans can be picked in #""_nC_2# ways,

which is the the number (no.) of favourable outcomes for the

event in question.

Further, there are #8# jellybeans in the bag, so, #2# out of

these can be selected in #""_8C_2# ways, which is the total no. of

outcomes for the event.

This gives us the prob. of the event as #(""_nC_2)/(""_8C_2)#.

Given that, this prob. is #3/14," we have," (""_nC_2)/(""_8C_2)=3/14#.

#:. {(n(n-1))/(1*2)}-:{(8*7)/(1*2)}=3/14#.

#:. n(n-1)=8*7*3/14=12#.

#:. n(n-1)=4*3=4(4-1), or, -3(-3-1)#.

#:. n=4, or, -3," which is inadmissible"#.

#:. n=4#.