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Eva8 [605]
3 years ago
10

A bag contains n blue and m red marbles. You randomly pick a marble from the bag, write down its color, and then put the marble

back in the bag. This process is repeated until you pick either two consecutive blue or two consecutive red marbles. Given that the process stopped because you picked two consecutive blue marbles, what is the probability that the first marbled you picked was blue
Mathematics
1 answer:
Oksana_A [137]3 years ago
3 0

Answer:

(mn+n²)/(m+n)

Step-by-step explanation:

probability of blue marble= n/(n+m)

probability of red marble= m/(n+m)

probability that process stops = Probability of both blue + probability of both red=  n/(n+m) × n/(n+m) + m/(n+m)×m/(n+m)

                        = (n²+m²)/(n+m)²

P(1st marbel is blue)= P(blue and red) + P(blue and blue)

                                  = mn/(n+m) + n²/(n+m)

                                   = (mn+n²)/(m+n)

P(1st marble is blue | process stops)= ( (mn+n²)/(m+n)× (n²+m²)/(n+m)²)/ ((n²+m²)/(n+m)²)

= (mn+n²)/(m+n)

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Step-by-step explanation:

Suppose that x, y are the the length and width

Area=x*y=80

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3 0
2 years ago
Read 2 more answers
OM , ON and OP are the angle bisectors of ∠AOB, ∠BOC, and ∠COD respectively. ∠AOD and ∠BOE are straight angles.
Orlov [11]

Find m∠BOC, if m∠MOP = 110°.

Answer:

m∠BOC= 40 degrees

Step-by-step explanation:

A diagram has been drawn and attached below.

  • OM bisects AOB into angles x and x respectively
  • ON bisects ∠BOC into angles y and y respectively
  • OP bisects ∠COD into angles z and z respectively.

Since ∠AOD is a straight line

x+x+y+y+z+z=180 degrees

2x+2y+2z=180^\circ

We are given that:

m∠MOP = 110°.

From the diagram

∠MOP=x+2y+z

Therefore:

x+2y+z=110°.

Solving simultaneously by subtraction

2x+2y+2z=180^\circ

x+2y+z=110°.

We obtain:

x+z=70°

Since we are required to find ∠BOC

∠BOC=2y

Therefore from x+2y+z=110° (since x+z=70°)

70+2y=110

2y=110-70

2y=40

Therefore:

m∠BOC= 40 degrees

3 0
3 years ago
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