Suppose a group of research proposals was evaluated by a panel of experts to decide whether or not they were worthy of funding. when these same proposals were submitted to a second independent panel of experts, the decision to fund was reversed in 40% of the cases. if the probability that a proposal is judged worthy of funding by the first panel is 0.2, what are the probabilities of these events? a. a worthy approval is approved by both panels b. a worthy approval is disapproved by both panels c. a worthy approval is approved by one panel

(a) 0.12 (b) 0.32 (c) 0.56

Step-by-step explanation:

The  sample outcomes are Funded or Unfunded. Total  sample space is given by:

2²= 4

Fund = F

Unfunded =  U

P (F) ist panel = 0.2

P (U) ist panel = 0.8

P (F) 2nd panel = 0.6

P (U) 2nd panel = 0.4

TOTAL SAMPLE SPACE

Ist Panel                Second Panel

F                                  F

F                                  U

U                                 F

U                                 U

(a) Probability of  both panel approval = P (FF)

                                                                =  0.2 x 0.6

                                                                =  0.12

(b) Probability of approval disapproved by both panels = P (UU)

                                                                                            = 0.8 x 0.4

                                                                                            = 0.32

(c) Probability of a worthy disapproval by one panel = P(FU) + P(UF)

                                         = (0.2 x 0.4) +(0.8 x 0.6)

                                         =  0.08 + 0.48

                                         =  0.56

12/11c

or

12

c

11

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°