Four students sit a typing test?

Question

a) The probability that anna passes the test is 1/2 (half).
The probability that boris passes the test is 4/9

Calculate the probability that both anna and boris pass the test. Give your answer in its simplest form.

b) The probability that Chloe passes the test 3/5
The probability that both Chloe and Danny pass the test 7/15.

Calculate the probability that both Chloe and Danny fail the test.

Answer 1

a)
The probability Anna passes is 1/2
The probability Boris passes is 4/9

The probability that they both pass is the product of the two probabilities:
Both = 1/2 * 4/9 = 4/18
Reduce this to 2/9:

Probability they both pass = 2/9

b)
First, a common mistake would be to assume that the chance that they both fail is 1 minus the probability they both pass, but it isn't. Instead, first figure the probability that Danny passes. This is just the reverse of the problem above.

The probability Chloe passes = 3/5
The probability Danny passes = d
The probability they both pass = 7/15

3/5 * d = 7/15
d = 7/15 / 3/5
d = 7/15 * 5/3
d = 35/45
d = 7/9

So the probability that Danny passes is 7/9

To figure the chance they both fail, first figure their individual probabilities of failure.
Probability that Chloe fails = 1 - 3/5 = 2/5
Probability that Danny fails = 1 - 7/9 = 2/9

Probability they both fail is the product of 2/5 and 2/9.

Chance they both fail is:
2/5 (Chloe fails) x 2/9 (Danny fails) = 4/45

Answer 2

First question, straight probabilities, 1/2*4/9 = 2/9

Second question, a little more complicated

Probability that Chloe passes = 3/5

Probabilty that they both pass = 7/15

therefore the probability that danny passes is

3/5 * D = 7/15 (substituting danny's probability for D)

Solve for D

D = 7/15 / 3/5 = 7/9

Probability that danny fails = 1- 7/9 = 2/9

Probabilty that Chloe fails = 1- 3/5 = 2/5

2/9*2/5 = 4/45 and hence the probabilty that they both fail

Answer 3

a) 1/2 x 4/9 = 1/9
Remember the rule of using multiplication for 'and' and addition for 'or' conditions. Since you want both anna AND boris to pass the test, you simply multiply them.

b) I think one common mistake to do would be to subtract 7/15 from 1. Rather, find the probability of Danny passing the test, by dividing 7/15 with 3/5 = 7/9.
Probability of Danny failing:
1-7/9 = 2/9
Probability of Chloe failing:
1-3/5 = 2/5
Proability of bothfailing:
2/5 x 2/9 = 4/45

Answer 4

a) the probability that both anna and boris
pass the test is 1/2*4/9=2/9

b)the probaility that chloe and danny pass the test
is 7/15
the probability of chloe passes the test is 3/5
let the probability of danny passing the test
be x
3x/5=7/15
>>>>x=7/9

therefore the probability of danny
passing the test is 7/9

the probability of chloe failing the test
is(1-3/5)=2/5
the probability of danny failing the test
is(1-7/9)=2/9
the probability of both danny and chloe
failing the test is (2/5*2/9)=4/45

i hope that this helps

Answer 5

a) P(anna and boris pass) = (1/2) x (4/9) = 2/9

b)
P(chloe and danny pass) = 7/15
P(chloe passes) x P(danny passes) = 7/15
3/5 x P(danny passes) = 7/15
P(danny passes) = (7/15) x (5/3) = 7/9

P(chloe and danny fail)
= (1 - 3/5) x (1 - 7/9)
= (2/5) x (2/9)
= 4/45

Answer 6

i imagine you should determine out what is going on. i understand she suggested she replaced into tremendous, yet A's and B's and then getting D's could propose that there is a subject matter. i'm fairly shy I frequently smiled at instructors except that i replaced into quiet and somewhat ever suggested some thing. that doesn't mean some thing is incorrect in spite of the actuality that. If she is appearing diverse then sure, i'd do some thing.

Answer 7

I think they both passed the test why the hell do we want to know the rest