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Alekssandra [29.7K]
3 years ago
12

A bag contains two coins, one for which the probability of heads is equal to 1 and one for which the probability of heads is equ

al to p. A coin is selected at random, and three independent tosses of this coin result in three heads. What is the probability that a further independent toss of this coin will produce a head?a. p4/1 + p3.b. p3 - p2/1 + p3.c. p3/1 - p.d. 1/1 + p3.e. 1 + p4/1 + p3.
Mathematics
1 answer:
wlad13 [49]3 years ago
5 0

Answer: Option E is the correct answer; (1 + p⁴) / (1 + p³)

Step-by-step explanation:

P (3 head) = P(first and 3 heads) + P(second coin and 3 heads)

= (1/2)×1³ + (1/2)× p³ = (1/2) × (1 + p³)

therefore P(first coin given 3 heads) = (1/2)×1³/ ((1/2)×(1 + p³))

= 1 / (1 + p³)

Also P( second coin given 3 heads) = p³ /(1 + p³)

therefore P(4th toss in heads given first 3 are heads)  will be;

= P(first and 4th toss heads) + P(second and 4th toss heads)

=(1/( 1 + p³ )) × 1 + p³ / (1+p³) × p

= (1 + p⁴) / (1 + p³)

Therefore Option E is the correct answer

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Nico was stunned when he opened the mail.Here was a check for $332.50 this is the interest he earned on his investment.One year
Mazyrski [523]

Answer:

Investment A = 3650

Investment B = 1350

Step-by-step explanation:

Given that:

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Total Principal invested = 5000

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Time = 1 year

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Investment B:

Rate = 3%

Time = 1 year

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From (1)

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0.08(5000 - b) + 0.03b = 332.50

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7 0
3 years ago
Find the x- and y-intercepts of the following line: 4x − 3y = 12
Slav-nsk [51]

Answer:

x-intercept: (3,0)

y-intercept: (0,-4)

Step-by-step explanation:

To find the x and y-intercepts, we first need to understand what they are. X and y-intercepts are points on the line that passes through the x-axis and y-axis. When a point is an x-intercept, it passes through the x-axis. This means the x-coordinate is an integer, while the y-coordinate is always 0. This can be denoted by (x,0). When a point is a y-intercept, it passes through the y-axis. This means the y-coordinate is an integer, while the x-coordinate is always 0. This can be denoted by (0,y).

Now that we know what x and y-intercepts are, we can plug in x=0 and y=0 to find the intercepts.

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4x-3y=12            [plug in y=0]

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---------------------------------------------------------------------------------------------------------

y-intercept

4x-3y=12            [plug in x=0]

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0-3y=12             [subtract both sides by 0]

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y=-4

Therefore, the x-intercept is (3,0) and y-intercept is (0,-4).

3 0
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I need these done as quick as possible and i have no clue what to do.
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Answer:

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