Question

Joshua is playing darts. He's not very good, so the probability that he'll score a bulls-eye is only 0.5 % . He has a 8 % of hitting the triple ring, a 25 % chance of hitting the double ring, and a 48 % chance of hitting the single ring. Also, there is a 18.5 % chance that he'll miss the target altogether. If he throws 6 darts, what is the probability that he hits the triple ring exactly once and the single ring exactly three times?

which one is correct?

2.8%

5.5%

8.6%

10.3%

15.5%

Answer 1

Joshua is playing darts.

He hits the bulls eye 0.5% of the times; so chance of hitting the bulls eye is 0.005.

He hits the triple rings 8% of the times; so chance of hitting the triple ring is 0.08.

He hits the double rings 25% of the times; so chance of hitting the double ring is 0.25.

He hits the single ring 48% of the times; so chance of hitting the single ring is 0.48.

He misses altogether 18.5% of the times; so chance of altogether missing is 0.185.

Joshua throws 6 darts. We have to find the probability that he hits the triple ring exactly once, and the single ring exactly thrice.

Now, the single ring throws are 3 in number; these 3 can be selected from 6 throws in (6 C 3), ie. 20 ways.

The triple ring throw is one in number; this 1 can be selected from the rest 3 throws in 3 ways.

The rest two throws can give any outcome, except a single ring or a triple ring.

So, these two throws have probability 1-0.08-0.48, ie. 0.44.

Now, the single ring throws occur thrice each with chance 0.48; the triple ring throw occurs with chance 0.08.

So, the equired probability is

Which is approximately,

  

So, the corresponding percentage is 0.103*100, ie. 10.3%.

So, the answer is option (D) 10.3%.