2
$\begingroup$

John keeps a weather chart he records each day as either wet or dry it is dry one day the probability it will be dry the next day is $\frac{4}{5}$. it is wet one day the probability it will be wet the next day is $\frac{2}{5}$ the $31$st March is dry

I have done the tree diagram

I need help on finding the probability that 2nd April will be dry

I have said that the probability of it being wet on 2nd April is 2/5 this means that the probability of it being dry on 2nd April is 3/5 because probabilities add up to 1 is that right?

if it talks about at least one of the days 1st and 2nd april will be dry how do I solve that?

  • 0
    If you have done the tree diagram, what's stopping you? Just find the probability for each end ("leaf") that means 2nd of April is dry, and add them up. – 2017-01-22
  • 0
    How do you get $\frac 35$? – 2017-01-22
  • 1
    Add tree diagram. – 2017-01-22

2 Answers 2

1

Either the $1$st of March will be dry and the $2$nd will be dry, or the $1$st of March will be wet and the $2$nd will be dry.

The first case happens with probability $\frac{4}{5}\times \frac{4}{5} = \frac{16}{25}$.

The second case happens with probability $(1-\frac{4}{5})\times (1-\frac{2}{5}) = \frac{3}{25}$.

Sum them together to get the answer: $\frac{19}{25}$.

0

Case 1 - If day is dry.

Next day is dry probability $\frac45$

Next day is wet probability $\frac15$

Case 2 - If day is wet.

Next day is wet probability $\frac25$

Next day is dry probability $\frac35$

Now 31st march is dry. So we have 1st april either dry or wet and 2nd april is dry.

If 1st april dry then provability $\frac45$ and 2nd is also dry $\frac45$.

$\frac45 \times \frac45 = \frac{16}{25}$

If 1st april wet then provability $\frac15$ as wet after dry and 2nd is dry $\frac35$ as dry after wet.

$\frac15 \times \frac35 = \frac{3}{25}$

Combining we have

$\frac{16}{25} + \frac3{25} = \frac{19}{25}$

  • 0
    If any doubt please ask. – 2017-01-22
  • 0
    if it talks about at least one of the days 1st and 2nd april will be dry how do I solve that? – 2017-01-22
  • 0
    Please ask another question. Promise I will try to solve that. – 2017-01-22
  • 0
    And about doubt you can ask here. Because another question you are asking needs explanation and I will explain you in answer. – 2017-01-22